Inverse operation - operations that undo each other: addition and subtraction, or multiplication and division.
Addition Property of Equality- the property that states that if you add the same number to both sides of an equation, the new equation will have the same solution.
Subtraction Property of Equality- The property that states that if you subtract the same number from both sides of an equation, the new equation will have the same solution.
Section 4- Solving Equations by Multiplying or Dividing
Multiplication Property of Equality- the property that states that if you multiply both sides of an equation by the same number, the new equation will have the same solution.
Division Property of Equality- the property that states if you divide both sides of an equation by the same nonzero number, the new equation will have the same solution.
Section 5- Solving Simple Inequalities
Inequality- A mathematical sentence thats shows the relationship between quantities that are not equivalent.
Simplify- to write a fraction or expression in simplest form.
1-7
Ordered Pair- a pair of numbers that can be used t locate a point on a cordinate plane.
1-8
Coordinate Plane- (coordinate grid) a plane formed by the intersection of a horizontal number line called the x-axis and a vertical number line called the y-axis.
Biased Sample- a sample that does not fairly represent the population.
Random Sample- a sample in which each individual or object in the entire population has an equal chance of being selected.
Systematic Sample- a sample of a population that has been selected using a pattern.
Stratified Sample- a sample of a population that has been divided into subgroups.
4-2
Steam-and-Leaf Plot- a graph used to organize and display data so that the frequencies can be compared.
Back- to- Back Stem-and-Leaf Plot- a stem-and-leaf plot that compares two sets of data by displaying one set of data to left of the stem and the other to the right.
4-3
Mean- the sum of a set of data divided by the number of items in the data set: also called average.
Median- the middle number, or the mean (average) of the two middle numbers, in an ordered set of data.
Mode- the number or numbers that occur most frequently in a set of data: when all numbers occur with the same frequency, we say there is no mode.
Outlier- a value much greater or much less than the others in a data set.
4-4
Variability- the spread of values in a set of data.
Range (in statistics)- the difference between the greatest and least values in a data set.
Quartile - three values, one of which is the median, that divided a data set into fourths.
Box-and-whisker plot- a graph that displays the highest and lowest quarters of data as whiskers, the middle two quarters of the data as a box, and the median.
4-5
Bar Graph - a graph that uses vertical or horizontal bars to display data.
Frequency Table- a table that lists items together according to the number of times, or frequency, that the items occur.
Histogram- a bar graph that shows the frequency of data within equal intervals.
Line Graph - a graph that uses line segments to show how data changes.
4-7
Scatter Plot- a graph with points plotted to show a possible relationship between two sets of data.
Correlation- the description of the relationship between two data sets.
Line of Best Fit - a straight line that comes closest to the points on a scatter plot.
Vertical Angles- a pair of opposite congruent angles formed by intersecting lines; on a polyhedron, the intersection of three or more faces; on a cone or pyramid, the top point.
Rotation Symmetry- a figure has a rotational symmetry if it can be rotated less than 360 degrees around a central point and coincide with the original figure.
5-9
Tessellation- a repeating pattern of plane figures that completely cover a plane with no gaps or overlaps.
Edge - the line segment along which two faces of a polyhedron intersect.
Vertex- on an angle, or polygon, the point where two sides intersect; on a polyhedron, the intersection of three or more faces; on a cone or pyramid, the top point.
Perspective - a technique used to make three-dimensional objects appear appear to have depth and distance on a flat surface.
Vanishing Point - in a perspective drawing, a point where lines running away from the viewer meet.
Horizon Line - a horizontal line that represents the viewer's eye level.
6-6
Prism- a polygon that has two congruent, polygon-shaped bases and other faces that are all parallelograms.
Cylinder - a three-dimensional figure with two parallel, congruent circular bases connected by a curved lateral surface.
6-7
Pyramid- a polyhedron with a polygon base and triangular sides that all meet at a common vertex.
Cone - a three-dimensional figure with one vertex and one-circular base.
6-8
Surface Area- the sum of the areas of the faces, or surface, of a three-dimensional figure.
Lateral Face - in prism or a pyramid, a face that is not a base.
Lateral Surface- in a cylinder, the curved surface connecting the circular bases; in a cone, the curved surface that is not a base.
6-9
Slant Height- the distance from the base of a cone to its vertex, measured along the lateral surface.
Regular Pyramid - A pyramid whose base is a regular polygon and whose lateral faces are all congruent.
Right Cone- a cone in which a perpendicular line drawn from the base to the tip (vertex) passes through the center of the base.
6-10
Sphere - a three-dimensional figure with all points the same distance from the center.
Chapter 1- Algebra Toolbox
Section 1- Variables and Expressions
Section 3- Solving Equations by Adding or Subtracting
Section 4- Solving Equations by Multiplying or Dividing
- Multiplication Property of Equality- the property that states that if you multiply both sides of an equation by the same number, the new equation will have the same solution.
- Division Property of Equality- the property that states if you divide both sides of an equation by the same nonzero number, the new equation will have the same solution.
Section 5- Solving Simple Inequalities- Inequality- A mathematical sentence thats shows the relationship between quantities that are not equivalent.
- Algebraic Inequality- An inequality that contains at least one variable.
- Solution of an Inequality- A value or values that make an inequality true.
- Solution Set- the set of values that make a statement true.
1-6- Term- (in an expression) the parts of an expression that are added or subtract.
- Like Term- Two or more terms that have the same variables raised to the same power.
- Equivalent Expression- have the same value for all values of the variable.
- Simplify- to write a fraction or expression in simplest form.
1-7- Ordered Pair- a pair of numbers that can be used t locate a point on a cordinate plane.
1-8- Coordinate Plane- (coordinate grid) a plane formed by the intersection of a horizontal number line called the x-axis and a vertical number line called the y-axis.
- X-axis- a horizontal axis on a coordinate plane.
- Y-axis- a vertical axis on a coordinate plane.
- X-coordinate- the first number in an ordered pair; it tells the distance to move right or left from the origin.
- Y-coordinate- the second number in an ordered pair; it tells the distance to move up or down from the origin.
- Origin- the point where the x-axis and y-axis intersect on the coordinate plane.
- Graph of an Equation- a graph of the set of ordered pairs that are solutions of the equation.
2-1- Integer- the set of whole numbers and their opposites.
- Opposite- two numbers that are an equal distance from zero on the number line; also called additive inverse.
- Absolute value - the distance of a number from zero on a number line.
2-6- Power- a number produced by raising a base to an exponent.
- Exponential Form - a number is in exponential form when it is written with a base and an exponent.
- Exponent - the number that indicates how many times the base is used as a factor.
- Base (in numeration) - when a number is raised to power, the number that is used as a factor is the base.
2-9- Scientific Notation - a method of writing very large in a or very small numbers by using powers of 10.
3-1- Rational Number - any number that can be expressed as a ratio of to integers.
- Relatively Prime - two numbers are relatively prime if their greatest common factor (GCF) is 1.
3-4- Reciprocal - One of two numbers whose product is 1; also called multiplication inverse.
3-5- Least Common Denominator (LCD) - the least common multiple of two or more denominators.
3-8- Principal Square Root - the nonnegative square root of a number.
- Perfect Square- a square of a whole number.
3-10- Irrational Number- a number that cannot be expressed as a ratio of two integers or as a repeating or termination decimal.
- Real Number- a rational or irrational number.
- Destiny Property of Real Number- the property that states that between any two real numbers, there is always another real number.
4-1- Population- the entire group of objects or individuals considered for survey.
- Sample- a part of the population.
- Biased Sample- a sample that does not fairly represent the population.
- Random Sample- a sample in which each individual or object in the entire population has an equal chance of being selected.
- Systematic Sample- a sample of a population that has been selected using a pattern.
- Stratified Sample- a sample of a population that has been divided into subgroups.
4-2- Steam-and-Leaf Plot- a graph used to organize and display data so that the frequencies can be compared.
- Back- to- Back Stem-and-Leaf Plot- a stem-and-leaf plot that compares two sets of data by displaying one set of data to left of the stem and the other to the right.
4-3- Mean- the sum of a set of data divided by the number of items in the data set: also called average.
- Median- the middle number, or the mean (average) of the two middle numbers, in an ordered set of data.
- Mode- the number or numbers that occur most frequently in a set of data: when all numbers occur with the same frequency, we say there is no mode.
- Outlier- a value much greater or much less than the others in a data set.
4-4- Variability- the spread of values in a set of data.
- Range (in statistics)- the difference between the greatest and least values in a data set.
- Quartile - three values, one of which is the median, that divided a data set into fourths.
- Box-and-whisker plot- a graph that displays the highest and lowest quarters of data as whiskers, the middle two quarters of the data as a box, and the median.
4-5- Bar Graph - a graph that uses vertical or horizontal bars to display data.
- Frequency Table- a table that lists items together according to the number of times, or frequency, that the items occur.
- Histogram- a bar graph that shows the frequency of data within equal intervals.
- Line Graph - a graph that uses line segments to show how data changes.
4-7- Scatter Plot- a graph with points plotted to show a possible relationship between two sets of data.
- Correlation- the description of the relationship between two data sets.
- Line of Best Fit - a straight line that comes closest to the points on a scatter plot.
5-1- Point- an exact location in space.
- Line - a straight path that extends without end in oppos
Insert Link
ite directions. - Plane- a flat surface that extends forever.
- Segment - a part of a line between two endpoints.
- Ray - a part of a line that starts at one endpoint and extends forever.
- Angle- a figure formed by two rays with a common endpoint called the vertex.
- Right Angle- an angle that measures 90 degrees.
- Acute Angle - an angle that measures less than 90 degrees.
- Obtuse Angle- an angle whose measures is greater than 90 degrees but less than 180 degrees.
- Complementary Angles - two angles whose measures add to 90 degrees.
- Supplementary Angles - two angles whose measures have a sum of 180 degrees.
- Congruent- having the same size and shape.
- Vertical Angles- a pair of opposite congruent angles formed by intersecting lines; on a polyhedron, the intersection of three or more faces; on a cone or pyramid, the top point.
5-2- Parallel Lines- lines in a plane that do not intersect.
- Perpendicular Lines - lines that intersect ti form right angles.
- Transversal- a line that intersects two or more lines.
5-3- Triangle Sum Theorem - the theorem that states that the measures of the triangle add up to 180 degrees.
- Acute Triangle- a triangle with all angles measuring less than 90 degrees.
- Right Triangle- a triangle containing a right angle.
- Obtuse Triangle- a triangle containing one obtuse angle.
- Equilateral Triangle- a triangle with three congruent sides.
- Isosceles Triangle - a triangle with at least two congruent sides.
- Scalene Triangle- a triangle with no congruent sides.
5-4- Polygon- a closed plane figure formed by three or ore line segments that intersect only at their endpoints (vertices).
- Regular Polygon- a regular with congruent sides angles.
- Trapezoid- a quadrilateral with exactly one pair of parallel sides.
- Parallelogram - a quadrilateral with two pairs of parallel sides.
- Rectangle- a parallelogram with four right angles.
- Rhombus- a parallelogram with all sides congruent.
- Square - a rectangle with four congruent sides.
5-5- Slope- a measure of the steepness of a line on a graph; the rise divided by the run.
- Rise- the verticle change when the slope of a line is expressed
- Run- the horizontal change when the slope of a line is expressed as the ratio "rise over run".
5-6- Correspondence- the relationship between two or more objects that are matched.
5-7- Transformation- a change in size or position of a figure.
- Translation- a movement (slide) of a figure along a straight line.
- Rotation- a transformation in which a figure is turned around a point.
- Center of Rotation- the point about which a figure is rotated.
- Reflection- a transformation of a figure that flips the figure across a line.
- Image- a figure resulting from a transformation.
5-8- Line Symmetry- a figure has a line symmetry if one half is a mirror-image of the other half.
- Line of Symmetry - the imaginary "mirror" in line symmetry.
- Rotation Symmetry- a figure has a rotational symmetry if it can be rotated less than 360 degrees around a central point and coincide with the original figure.
5-9- Tessellation- a repeating pattern of plane figures that completely cover a plane with no gaps or overlaps.
- Regular tessellation - a tessellation formed by using regular polygons.
- Semiregular tessellation - a tessellation formed with two or more regular polygons in which every vertex is identical.
6-1- Perimeter- the distance around a polygon.
- Area - the number of square units needed to cover a given surface.
6-3- Pythagorean Theorem - in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
- Leg- in a right triangle, the sides that include the right angle; in an isosceles triangle, the pair of congruent sides.
- Hypotenuse- in a right triangle, the side opposites the pair of congruent sides.
6-4- Circle - the set of all points in a plane that are the same distance from a given point called the center.
- Radius - a line segment with one endpoints at the center of the circle and the other endpoint on the circle, or the length of that segments.
- Diameter- a line segment that passes through the center of a circle and has endpoints on the circle, or the length of that segment.
- Circumference - the distance around a circle.
6-5- Face- a flat surface of a polyhedron.
- Edge - the line segment along which two faces of a polyhedron intersect.
- Vertex- on an angle, or polygon, the point where two sides intersect; on a polyhedron, the intersection of three or more faces; on a cone or pyramid, the top point.
- Perspective - a technique used to make three-dimensional objects appear appear to have depth and distance on a flat surface.
- Vanishing Point - in a perspective drawing, a point where lines running away from the viewer meet.
- Horizon Line - a horizontal line that represents the viewer's eye level.
6-6- Prism- a polygon that has two congruent, polygon-shaped bases and other faces that are all parallelograms.
- Cylinder - a three-dimensional figure with two parallel, congruent circular bases connected by a curved lateral surface.
6-7- Pyramid- a polyhedron with a polygon base and triangular sides that all meet at a common vertex.
- Cone - a three-dimensional figure with one vertex and one-circular base.
6-8- Surface Area- the sum of the areas of the faces, or surface, of a three-dimensional figure.
- Lateral Face - in prism or a pyramid, a face that is not a base.
- Lateral Surface- in a cylinder, the curved surface connecting the circular bases; in a cone, the curved surface that is not a base.
6-9- Slant Height- the distance from the base of a cone to its vertex, measured along the lateral surface.
- Regular Pyramid - A pyramid whose base is a regular polygon and whose lateral faces are all congruent.
- Right Cone- a cone in which a perpendicular line drawn from the base to the tip (vertex) passes through the center of the base.
6-10- Sphere - a three-dimensional figure with all points the same distance from the center.
- Hemisphere- a half of a sphere.
- Great Circle- a circle on a sphere such that the plane containing the circle passes through the center of the sphere.
7-1